Loop-Erasure of Plane Brownian Motion

Abstract

We use the coupling technique to prove that there exists a loop-erasure of a plane Brownian motion stopped on exiting a simply connected domain, and the loop-erased curve is the reversal of a radial SLE${}_2$ curve.

10 pages

References in corpus (5)

• The dimension of the SLE curves
• Conformal restriction: the chordal case
• Duality of Chordal SLE
• Reversibility of chordal SLE
• The scaling limits of planar LERW in finitely connected domains

Cited by in corpus (1)

• Loop-erased walks and random matrices